Showing papers on "K-epsilon turbulence model published in 1989"

Parameterization of Orography-Induced Turbulence in a Mesobeta--Scale Model

Abstract: The possibility of extending existing techniques for turbulence parameterization in the planetary boundary layer to attitude, orography-induced turbulence events is examined. Starting from a well-tested scheme, we show that it is possible to generalize the specification method of the length scales, with no deterioration of the scheme performance in the boundary layer. The new scheme is implemented in a two-dimensional version of a limited-area, numerical model used for the simulation of mesobeta-scale atmospheric flows. Three well-known cases of orographically induced turbulence are studied. The comparison with observations and former studies shows a satisfactory behavior of the new scheme.

Lagrangian statistics from direct numerical simulations of isotropic turbulence

Abstract: A comprehensive study is reported of the Lagrangian statistics of velocity, acceleration, dissipation and related quantities, in isotropic turbulence. High-resolution direct numerical simulations are performed on 643 and 1283 grids, resulting in Taylor-scale Reynolds numbers Rλ in the range 38-93. The low-wavenumber modes of the velocity field are forced so that the turbulence is statistically stationary. Using an accurate numerical scheme, of order 4000 fluid particles are tracked through the computed flow field, and hence time series of Lagrangian velocity and velocity gradients are obtained.The results reported include: velocity and acceleration autocorrelations and spectra; probability density functions (p.d.f.'s) and moments of Lagrangian velocity increments; and p.d.f.'s, correlation functions and spectra of dissipation and other velocity-gradient invariants. It is found that the acceleration variance (normalized by the Kolmogorov scales) increases as R½λ - a much stronger dependence than predicted by the refined Kolmogorov hypotheses. At small time lags, the Lagrangian velocity increments are distinctly non-Gaussian with, for example, flatness factors in excess of 10. The enstrophy (vorticity squared) is found to be more intermittent than dissipation, having a standard-deviation-to-mean ratio of about 1.5 (compared to 1.0 for dissipation). The acceleration vector rotates on a timescale about twice the Kolmogorov scale, while the timescales of acceleration magnitude, dissipation and enstrophy appear to scale with the Lagrangian velocity timescale.

Reynolds-number effects on the structure of a turbulent channel flow

Abstract: A high resolution, two component laser-Doppler anemometer has been used for turbulence measurements at a high data rate in a channel flow of water. Measurements of the velocity components in the stream direction and in a direction normal to the wall are reported over the Reynolds number range of 3000–40000. The combination of high spatial resolution and high data rates enabled accurate reconstruction of time dependent velocity traces. Long-time statistical averages of these signals clearly show that profiles of the dimensionless turbulence quantities such as turbulence intensities and Reynolds stress are strongly Reynolds-number dependent over a large part of the channel flow. For instance, in the Reynolds-number range of this investigation, it is shown that the fluctuating turbulence quantities do not scale with wall variables even as close as 15 viscous lengths from the wall. The velocity traces and associated power spectra exposed two phenomena which may explain the Reynolds number dependencies.

Advances in turbulence

Abstract: Contents: The State of Turbulence Research.- Contributions of Numerical Simulation Data Bases to the Physics, Modeling, and Measurement of Turbulence.- The Self-Preservation of Turbulent Flows and Its Relation to Initial Conditions and Coherent Structures.- Engineering Turbulence Models.- Chaos and the Onset of Turbulence.- Advances in Turbulence Measurement Techniques.- The Role of Smoke Visualization and Hot-Wire Anemometry in the Study of Transition.- Index.

Evaluation of turbulent transport and dissipation closures in second-order modeling

Abstract: We show that the turbulence statistics from our (96)3 large-eddy-simulation (LES) studies of a convective boundary layer are in excellent agreement with those from the Deardorff–Willis laboratory convection tank. Using these LES data, we evaluate contemporary parameterizations for turbulent transport and dissipation in second-order closure models of the convective boundary layer. The gradient-diffusion parameterization for turbulent transport fares poorly, due in large part to the direct influence of buoyancy. This leads to poor predictions of the vertical profiles of some turbulence statistics. We also find that the characteristic length scales for the mechanical and thermal dissipation rates typically used in second-order closure models are a factor of 2–3 too small; this leads to underpredictions of turbulence kinetic energy levels. Finally, we find that the flux and variance budgets for conservative scalars are substantially different in top-down and bottom-up diffusion. In order to reproduce...

Direct numerical simulation of stratified homogeneous turbulent shear flows

Abstract: The exact time-dependent three-dimensional Navier-Stokes and temperature equations are integrated numerically to simulate stably stratified homogeneous turbulent shear flows at moderate Reynolds numbers whose horizontal mean velocity and mean temperature have uniform vertical gradients. The method uses shear-periodic boundary conditions and a combination of finite-difference and pseudospectral approximations. The gradient Richardson number Ri is varied between 0 and 1. The simulations start from isotropic Gaussian fields for velocity and temperature both having the same variances. The simulations represent approximately the conditions of the experiment by Komori et al. (1983) who studied stably stratified flows in a water channel (molecular Prandtl number Pr = 5). In these flows internal gravity waves build up, superposed by hot cells leading to a persistent counter-gradient heat-flux (CGHF) in the vertical direction, i.e. heat is transported from lower-temperature to higher-temperature regions. Further, simulations with Pr = 0.7 for air have been carried out in order to investigate the influence of the molecular Prandtl number. In these cases, no persistent CGHF occurred. This confirms our general conclusion that the counter-gradient heat flux develops for strongly stable flows (Ri [approximate] 0.5–1.0) at sufficiently large Prandtl numbers (Pr = 5). The flux is carried by hot ascending, as well as cold descending turbulent cells which form at places where the highest positive and negative temperature fluctuations initially existed. Buoyancy forces suppress vertical motions so that the cells degenerate to two-dimensional fossil turbulence. The counter-gradient heat flux acts to enforce a quasi-static equilibrium between potential and kinetic energy. Previously derived turbulence closure models for the pressure-strain and pressure-temperature gradients in the equations for the Reynolds stress and turbulent heat flux are tested for moderate-Reynolds-number flows with strongly stable stratification (Ri = 1). These models overestimate the turbulent interactions and underestimate the buoyancy contributions. The dissipative timescale ratio for stably stratified turbulence is a strong function of the Richardson number and is inversely proportional to the molecular Prandtl number of the fluid.

Turbulence Control in Wall Flows

Abstract: Most of the detailed turbulence-structure data available pertain only to the simplest cases, involving zero pressure-gradient boundary layers and free-shear layers, and indicate that each disparate geometry possesses its own set of dominant nonlinear instabilities. Various boundary/input conditions act to modify these instabilities for low input levels; for stronger inputs, the basic instability modes/structures sustaining the turbulence field may be altered. Steady-state inputs are noted to be extremely effective in altering turbulence structures, in the directions of either amplification or diminution.

Computation of highly swirling confined flow with a Reynolds stress turbulence model

Abstract: The ability of a turbulence model to capture the interaction between swirl and the turbulent stress field is, therefore, crucial to the predictive performance of the computatinal scheme as a whole. A finite-volume procedure is used here to contrast the performance of the k-epsilon eddy-viscosity model with that of a Reynolds-stress transport closure. It is shown that the former returns a seriously excessive level of turbulent diffusion and misrepresents the experimentally observed flow characteristics. In contrast, the Reynolds-stress model successfully captures the subcritical nature of the flow by returning significantly lower levels of the shear stress components and predicts velocity and turbulence fields that are in good agreement with corresponding measurements. 22 references.

Renormalization group formulation of large-eddy simulations

Abstract: Perhaps the most distinguishing characteristic of high Reynolds number turbulent flows is their large range of excited space and time scales. In homogeneous turbulence, dissipation-scale eddies are of order R3/4 times smaller than energy-containing eddies, where R is the Reynolds number. In order to solve the Navier-Stokes equations accurately for such a turbulent flow, it is necessary to retain order (R3/4)3 spatial degrees of freedom. Also, since the time scale for significant evolution of homogeneous turbulence is of the order of the turnover time of an energy containing eddy, it is necessary to perform order R3/4 time steps to calculate for a significant evolution time of the flow. Even if these calculations require only O(1) arithmetic operations per degree of freedom per time step, the total computational work involved would be order R3, while the computer storage requirement would be R9/4. In this case, doubling the Reynolds number would require an order of magnitude improvement in computer capability. With this kind of operation and storage count, it is unlikely that forseeable advances in computers will allow the full numerical simulation of turbulent flows at Reynolds numbers much larger than Rλ = 0(100) already achieved (see BRACHET et al. [2]).

Turbulence structure of a boundary layer beneath a turbulent free stream

Abstract: Measurements have been made in the turbulent boundary layer on a flat plate in the presence of grid-generated free-stream turbulence with a wide range of lengthscales Complete balances of turbulent kinetic energy and shear stress have been evaluated, dissipation and pressure strain redistribution having been deduced by difference

Turbulence characteristics of sediment-laden flow

Abstract: Experiments are reported which were carried out in open channel flow in a laboratory flume; and turbulent structures of both clear water flow and sediment-laden flow, which were kept under exactly the same conditions, were measured, compared and analyzed. It was found that the various statistical parameters of turbulence measured in clear water flow are essentially consistent with those obtained by other researchers. The turbulent intensity decreases with increase in concentration. In sediment-laden flow, the probability density distribution and the autocorrelation coefficient are similar to those of the clear water flow. Turbulent frequency decreases and turbulent energy is concentrated to large-size eddies with low frequency. The longitudinal sizes of macroscale and microscale eddies increase. It was found that for a Newtonian flow with noncohesive particles, the fundamental turbulent structure has no essential change - only the turbulent intensity and frequency have some changes in magnitude. These and other findings are discsussed.

Direct simulation of a turbulent oscillating boundary layer

Abstract: The turbulent boundary layer under a freestream velocity that varies sinusoidally in time around a zero mean is considered. The flow has a rich variety of behaviors including strong pressure gradients, inflection points in the velocity profile, and reversal of the shear stress. A theory for the velocity- and stress profiles at high Reynolds number is formulated. Well-resolved direct Navier-Stokes simulations are conducted over a narrow range of Reynolds numbers. The flow is also computed over a wider range of Reynolds numbers using a new algebraic turbulence model. The results produced by the three approaches and by experiments are compared. Detailed phase-averaged statistical results from the direct simulations are provided to assist turbulence-model development.

Navier-Stokes analysis of solid propellant rocket motor internal flows

Abstract: A multidimensional implicit Navier-Stokes analysis that uses numerical solution of the ensemble-averaged Navier-Stokes equations in a nonorthogonal, body-fitted, cylindrical coordinate system has been applied to the simulation of the steady mean flow in solid propellant rocket motor chambers. The calculation procedure incorporates a two-equation (k-epsilon) turbulence model and utilizes a consistently split, linearized block-implicit algorithm for numerical solution of the governing equations. The code was validated by comparing computed results with the experimental data obtained in cylindrical-port cold-flow tests. The agreement between the computed and experimentally measured mean axial velocities is excellent. The axial location of transition to turbulent flow predicted by the two-equation (k-epsilon) turbulence model used in the computations also agrees well with the experimental data. Computations performed to simulate the axisymmetric flowfield in the vicinity of the aft field joint in the Space Shuttle solid rocket motor using 14,725 grid points show the presence of a region of reversed axial flow near the downstream edge of the slot.

Turbulence structure in a shock wave/turbulent boundary-layer interaction

Abstract: The boundary-layer turbulence structure in a two-dimensional 24-deg compression corner flow was investigated experimentally in the Princeton University 203 x 203-mm supersonic blowdown wind tunnel. The incoming conditions were M<» = 2.84, Re^/l = 6.5 x 10, and 60 = 26 mm. The results show that the maximum mass-flux turbulence intensity is amplified by a factor of about 5, whereas the mean mass flux increases by only 2 through compression. Probability density functions (pfd's) of the mass-flux fluctuations show that upstream the distributions are Gaussian-like and typical of a fully turbulent boundary layer. Behind the interaction, however, the distributions are bimodal, centering about a level indicative of the freestream mass flux and a lower level indicative of the mass flux near the wall. The unsteady shock motion does not appear to contribute signficantly to the turbulence amplification. It is suggested that the strong, bimodal mixing indicated in the pdf's is probably caused by the presence of large-scale motions associated with the instability of the inflectional velocity profiles observed downstream of the interaction. Space-time correlations of the mass flux and wall pressure were measured, as well as the level of intermittency of the boundary layer to further characterize the changes in the boundary-layer structure through the interaction.

The shearless turbulence mixing layer

Abstract: The interaction of two energy-containing turbulence scales is studied in the absence of mean shear. The flow, a turbulence mixing layer, is formed in decaying grid turbulence in which there are two distinct scales, one on either side of the stream. This is achieved using a composite grid with a larger mesh spacing on one side of the grid than the other. The solidity of the grid, and thus the mean velocity, is kept constant across the entire flow. Since there is no mean shear there is no turbulence production and thus spreading is caused solely by the fluctuating pressure and velocity fields. Two different types of grids were used: a parallel bar grid and a perforated plate. The mesh spacing ratio was varied from 3.3:1 to 8.9:1 for the bar grid, producing a turbulence lengthscale ratio of 2.4:1 and 4.3:1 for two different experiments. For the perforated plate the mesh ratio was 3:1 producing a turbulence lengthscale ratio of 2.2:1. Cross-stream profiles of the velocity variance and spectra indicate that for the large lengthscale ratio (4.3:1) experiment, a single scale dominates the flow while for the smaller lengthscale ratio experiments, the energetics are controlled by both lengthscales on either side of the flow. In all cases the mixing layer is strongly intermittent and the transverse velocity fluctuations have large skewness. The downstream data of the second, third and fourth moments for all experiments collapse well using a single composite lengthscale. The component turbulent energy budgets show the importance of the triple moment transport and pressure terms within the layer and the dominance of advection and dissipation on the outer edge. It is also shown that the bar grids tend toward self-similarity with downstream distance. The perforated plate could not be measured to the same downstream extent and did not reach self-similarity within its measurement range. In other respects the two types of grids yielded qualitatively similar results. Finally, we emphasize the distinction between intermittent turbulent penetration and turbulent diffusion and show that both play an important role in the spreading of the mixing layer.

The curvature of material surfaces in isotropic turbulence

Abstract: Direct numerical simulation is used to study the curvature of material surfaces in isotropic turbulence. The Navier–Stokes equation is solved by a 643 pseudospectral code for constant‐density homogeneous isotropic turbulence, which is made statistically stationary by low‐wavenumber forcing. The Taylor‐scale Reynolds number is 39. An ensemble of 8192 infinitesimal material surface elements is tracked through the turbulence. For each element, a set of exact ordinary differential equations is integrated in time to determine, primarily, the two principal curvatures k1 and k2. Statistics are then deduced of the mean‐square curvature M= (1)/(2) (k21+k22), and of the mean radius of curvature R=(k21+k22)−1/2. Curvature statistics attain an essentially stationary state after about 15 Kolmogorov time scales. Then the area‐weighted expectation of R is found to be 12η, where η is the Kolmogorov length scale. For moderate and small radii (less than 10η) the probability density function (pdf) of R is approximately uniform, there being about 5% probability of R being less than η. The uniformity of the pdf of R, for small R, implies that the expectation of M is infinite. It is found that the surface elements with large curvatures are nearly cylindrical in shape (i.e., ‖k1‖≫‖k2‖ or ‖k2‖≫‖k1‖), consistent with the folding of the surface along nearly straight lines. Nevertheless the variance of the Gauss curvature K=k1k2 is infinite.

The Prediction of Two-Phase Turbulence and Phase Distribution Phenomena Using a K-κ Model

Abstract: A closed-loop analysis of phase distribution is presented. This analysis is based on the use of a two-fluid model. It is shown that the treatment of the turbulence distribution in the continuous phase is crucial if accurate predictions are to be made. A K-κ model is used to model turbulence in this study. Finally, recommendations are made as to how the state-of-the-art can be advanced.

Turbulence Modeling in Noninertial Frames of Reference

Abstract: The effect of an arbitrary change of frame on the structure of turbulence models is examined from a theoretical standpoint It is proven, as a rigorous consequence of the Navier-Stokes equations, that turbulence models must be form invariant under arbitrary translational accelerations of the reference frame and should only be affected by rotations through the intrinsic mean vorticity A direct application of this invariance property along with the Taylor-Proudman theorem, material frame-indifference in the limit of two-dimensional turbulence, and Rapid Distortion Theory is shown to yield powerful constraints on the allowable form of turbulence models Most of the commonly used turbulence models are demonstrated to be in violation of these constraints and consequently are inconsistent with the Navier-Stokes equations in noninertial frames Alternative models with improved noninertial properties are developed and some simple applications to rotating turbulent flows are considered

k-ε Predictions of Heat Transfer in Turbulent Recirculating Flows Using an Improved Wall Treatment

Abstract: Different wall treatments, proposed in conjunction with the k-e turbulence model to predict heat or mass transfer rates, are critically reviewed. Published comparisons with experimental data for recirculating flows show that, in most cases, Nusselt or Sherwood numbers are not well predicted in the reattachment and redevelopment regions by methods based on conventional wall functions. The use of low-Reynolds-number models leads to even more unreliable results. A new treatment is proposed that formally retains classic wall functions and scaling based on the near-wall turbulent kinetic energy, but allows the nondimensional thickness of the viscous sublayer to vary as a function of the local turbulence intensity. The rationale for this approach, and its physical meaning, are discussed in the context of recent near-wall turbulence data. Using the k-e computer code FLOW3D, results are compared with those from a standard treatment, and with experimental data, for different geometries including single an...

Near-wall k-epsilon turbulence modeling

Abstract: The flow fields from a turbulent channel simulation are used to compute the budgets for the turbulent kinetic energy (k) and its dissipation rate (epsilon). Data from boundary layer simulations are used to analyze the dependence of the eddy-viscosity damping-function on the Reynolds number and the distance from the wall. The computed budgets are used to test existing near-wall turbulence models of the k-epsilon type. It was found that the turbulent transport models should be modified in the vicinity of the wall. It was also found that existing models for the different terms in the epsilon-budget are adequate in the region from the wall, but need modification near the wall. The channel flow is computed using a k-epsilon model with an eddy-viscosity damping function from the data and no damping functions in the epsilon-equation. These computations show that the k-profile can be adequately predicted, but to correctly predict the epsilon-profile, damping functions in the epsilon-equation are needed.

Comparative study of turbulence models in predicting turbulent pipe flow. I - Algebraic stress and k-epsilon models

Abstract: Developing turbulent pipe flow in a smooth circular pipe with a length of about 80 diameters is simulated at Reynolds numbers of 10,000, 38,000, 90,000 and 380,000, using seven different turbulence models. The governing equations are solved in their fully elliptic forms. The predictions for the velocity, turbulence kinetic energy, dissipation rate and Reynolds stress fields are compared to available experimental data and the relative performance of the models is assessed. This paper is Part II of a two-part study, in which a total of eleven turbulence models are compared.

Simulation of free surface effects on turbulence with a Reynolds stress model

Abstract: The main features of the highly anisotropic turbulence in the region of vanishing shear near the free surface of two-dimensional channel flow have been calculated using a Reynolds-stress transport model with surfaceeffect terms in the pressure-strain-rate correlation. The form of these terms is identical for solid and free surfaces. For a free surface, however, the surface-proximity function is an order of magnitude greater than the function for a rigid surface.

Measurements of turbulence in the benthic boundary layer over a gravel bed

Abstract: It is now generally recognized that the mathematical description of sediment dynamics will be improved through an understanding of geophysical turbulence. In this study, therefore, the turbulence characteristics of the benthic boundary layer over coarse sediments are examined as a step towards the realization of such a description. Examination of the turbulence has been conducted using spectral, correlation, quadrant and statistical analyses, and a number of features have been identified. Mean eddy length scales obtained using spectral and autocorrelation techniques were found to be similar. The interpretation of the duration and interval between the intermittent ‘bursting’ events, scaled using outer flow variables, was found to be dependent upon the sampling interval. Autocorrelation analysis revealed a high correlation between bedload transport and the instantaneous horizontal flow component rather than instantaneous kinematic stress. From the standpoint of developing prognostic transport models based on physically realistic benthic flow processes, it is considered that turbulence measurements will lead to such formulation.